map(LieDerivation) -- get the map in the definition of a Lie derivation

Synopsis

Function: map
Usage:

f = map(d)
Inputs:
- d, an instance of the type LieDerivation,
Optional inputs:
- Degree => ..., default value null,
- DegreeLift => ..., default value null,
- DegreeMap => ..., default value null,
Outputs:
- f, an instance of the type LieAlgebraMap,

Description

The optional inputs given above are not relevant for Lie algebras. If $d$ is a derivation $M \ \to\ L$, then there is defined a Lie algebra map $f: M \ \to\ L$, which determines the $M$-module-structure on $L$, and this map is represented by map(d).

i1 : L=lieAlgebra({x,y},Signs=>1)

o1 = L

o1 : LieAlgebra

i2 : M=lieAlgebra({a,b},Signs=>0,Weights=>{2,2})

o2 = M

o2 : LieAlgebra

i3 : f = map(L,M,{x x,x y})

o3 = f

o3 : LieAlgebraMap

i4 : d = lieDerivation(f,{2 x,-y})

o4 = d

o4 : LieDerivation

i5 : describe d

o5 = a => 2 x
     b =>  - y
     map => f
     sign => 1
     weight => {-1, 0}
     source => M
     target => L

i6 : d a b

o6 = 0

o6 : L

Ways to use this method: